Random, frequent demands to enter password, account locked when password entered

2 of my 3 iPhones (all SE 3d generation) randomly have popups demanding that the account password be entered. These happen when nothing is being done that should require entering the password, e.g. while trying to use the square app that has been open and in use for several minutes or a few hours. None of the 3 phones have any form of 2FA activated, nor face ID, nor passcode. Tapping to cancel turns off the popup, but it often returns within 1 to 2 seconds, sometimes repeating up to 10 times before it gives up. This can happen several times a day, or I may go several days with no demand for the password. These demands for the password disrupt work -- I cannot process a payment on the square app until the demands for password stop popping up. This has been happening for one of the phones as long as I can remember, the other started doing it a few months ago. I do not see this happening with the third phone, settings are the same on all to the best of my knowledge (although I have discovered settings sometimes have been changed when there is an iOS update).

On one of the phones every time I enter the correct password the account is locked. I go through the steps to unlock it by answering questions, then re-enter the same password that led to it being locked, the password is then accepted and the account is unlocked.

When downloading free apps from the app store I am being required to enter the password even though in Settings / Media & Purchases / Password Settings I have turned off the Require Password setting for Free Downloads.

So -- how can I stop these frequent demands for the password when nothing is being done to actually require it, and how can I stop the phone from being locked when the correct password has been entered?

Thanks to all who have helpful advice.